The kinematics of stars and planetary nebulae in early type galaxies provide vital clues to the enigmatic physics of their dark matter halos. We fit published data for fourteen such galaxies using a spherical, self-gravitating model with two components: (1) a Sersic stellar profile fixed according to photometric parameters, and (2) a polytropic dark matter halo that conforms consistently to the shared gravitational potential. The polytropic equation of state can describe extended theories of dark matter involving self-interaction, non-extensive thermostatistics, or boson condensation (in a classical limit). In such models, the flat-cored mass profiles widely observed in disc galaxies are due to innate dark physics, regardless of any baryonic agitation. One of the natural parameters of this scenario is the number of effective thermal degrees of freedom of dark matter (F_d) which is proportional to the dark heat capacity. By default we assume a cosmic ratio of baryonic and dark mass. Non-Sersic kinematic ideosyncrasies and possible non-sphericity thwart fitting in some cases. In all fourteen galaxies the fit with a polytropic dark halo improves or at least gives similar fits to the velocity dispersion profile, compared to a stars-only model. The good halo fits usually prefer F_d values from six to eight. This range complements the recently inferred limit of 7<F_d<10 (Saxton & Wu), derived from constraints on galaxy cluster core radii and black hole masses. However a degeneracy remains: radial orbital anisotropy or a depleted dark mass fraction could shift our models preference towards lower F_d; whereas a loss of baryons would favour higher F_d.
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